Calculus Archive: Questions from August 18, 2022
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Draw the region and find its area.
Dibuje la región y encuentre su área: \[ S=\left\{(x, y) / x \leq 1,0 \leq y \leq e^{x}\right\} \]3 answers -
\( \frac{d y}{d x}=x^{2} \sqrt{x-19} \) \[ y=\frac{2(x-19)^{\frac{5}{2}}}{105}\left(23 x^{2}+228 x+2,527\right)+C \] \[ y=\frac{2(x-19)^{\frac{5}{2}}}{15}\left(23 x^{2}+209 x+2.527\right)+C \] \[ y=\f1 answer -
\( \int \frac{3-\sin 2 x+x^{3} \cos ^{2} 2 x}{\cos ^{2} 2 x} d x \) \( \int\left(6 \operatorname{cosec}^{2} \frac{3}{2} x-\sec ^{2} 2 x+4 \cos 3 x\right) d x \) \( \int 32 \sin ^{2} x \cos ^{2} x d x1 answer -
1 answer
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For the given parametric equations, find the points \( (x, y) \) corresponding to the parameter values \( t=-2,-1,0,1,2 \). \[ \left.\begin{array}{ll} & x=3 t^{2}+3 t, \quad y=2^{t+1} \\ t=-2 & (x, y)1 answer -
For the given parametric equations, find the points \( (x, y) \) corresponding to the parameter values \( t=-2,-1,0,1,2 \). \[ \begin{array}{ll} & x=\ln \left(6 t^{2}+1\right), \quad y=\frac{t}{t+7} \1 answer -
28. \( \frac{d}{d x} \int_{2}^{x^{2}} \sqrt{2+\cos ^{3} t} d t \) 26. \( \int_{0}^{1} \frac{36}{(2 x+1)^{3}} d x \)1 answer -
1) Utilice la definición de la derivada para hallar \( \frac{d y}{d x} \) para la función \( f(x)=-x^{2}+4 x+5 \) 2) Determine la ecuación de la linea tangente a la función \( f(x)=-x^{2}+4 x+5 \)1 answer -
\[ \sum_{k=0}^{\infty}(x-7)^{k} \] A) \( \frac{1}{8+x} \) B) \( \frac{1}{8-x} \) C) \( -\frac{1}{8+x} \) D) \( \frac{1}{x-8} \)1 answer -
\( y^{\prime}=\left(y^{2}-1\right)\left(e^{y}-2\right) \) where, \( y(0)=\frac{3}{2} \) and \( y(0)=-4 \)1 answer -
1 answer
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3 answers
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Given \( f(x, y)=4 x^{2}-2 x^{2} y^{5}+y^{6} \) \( f_{x}(x, y)= \) \[ f_{y}(x, y)= \] \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \]3 answers -
3 answers
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1 answer
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Escoja la mejor contestacion: 1. Evaluar \( \int \sin ^{-1} x d x \) \[ \begin{array}{l} x \sin ^{-1} x+\sqrt{1-x^{2}}+C \\ x \sin ^{-1} x-\sqrt{1-x^{2}}+C \\ x \sin ^{-1} x+\sqrt{1+x^{2}}+C \\ x \cos1 answer -
Find \( y_{:}^{\prime} \) a) \( y=\frac{2 x^{2}+x}{3 x^{2}-x} \) b) \( y=\left(2 x-x^{3}\right)\left(x^{2}-x\right) \)1 answer -
(4) Evaluate the integral: a) \[ \int_{0}^{1} x\left(x^{2}+1\right)^{3} d x \] b) \[ \int_{1}^{3} \frac{4 x^{3}-5 x^{2}-3}{x^{2}} d x \]3 answers